| Rock type | Weight per volume (lb/ft3) | Cost per pound |
|---|---|---|
| Basalt | 180 | $0.18 |
| Granite | 165 | $0.09 |
| Limestone | 120 | $0.03 |
| Sandstone | 135 | $0.22 |
A city is planning to build a rock retaining wall, a monument, and a garden in a park. The table above shows four rock types that will be considered for use in the project. Also shown for each rock type is its weight per volume, in pounds per cubic foot (lb/ft3), and the cost per pound, in dollars. The equation gives the total cost, in dollars, of the rocks used in the project in terms of the number of ft3 of limestone, w, and the number of ft3 of basalt, z. All four rock types are used in the project. Which of the following is the best interpretation of 3,385.80 in this context?
Correct answer: A
Explanation
Choice A is correct. The table shows the cost of limestone is $0.03/lb, and the weight per volume for limestone is 120 lb/ft3. Therefore, the term represents the cost, in dollars, of w ft3 of limestone. Similarly, the term
represents the cost, in dollars, of z ft3 of basalt. The given equation shows that the total cost of all the rocks used in the project is $7,576.20. Since it’s given that all four rock types are used in the project, the remaining term, 3,385.80, represents the cost, in dollars, of the granite and sandstone needed for the project.
Choice B is incorrect. The cost of basalt and limestone needed for the project can be represented by . Choice C is incorrect. The cost of the basalt needed for the project can be represented by the expression
. Choice D is incorrect and may result from neglecting to include granite in the rock types used for the project.
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